This thesis studies dynamic trading strategies in portfolio choice problems. Investors seek to allocate their wealth among different investment opportunities. The optimal strategies are determined by various aspects related to risk attitudes of investors and dynamic conditions of financial markets. The risk-averse utility functions are used to characterize the investors risk preference. We consider three portfolio choice problems. The first model studies a portfolio choice problem with budget constraints. Borrowing and short-selling constraints are not allowed. We characterize the optimal dynamic policy for a two-period problem using an exponential utility function. Additionally, we compare myopic and static policies with dynamic policies for different conditions. Furthermore, we also study the optimality of dynamic and myopic policies for multi-period problems with HARA utility functions. Finally, we provide numerical examples in order to compare the different strategies’ performances. In the second model, we determine the optimal investment strategy for scenarios with both fixed and proportional transaction costs in a multi-period setting. The optimal decision for the single period problem can be characterized by three regions in which the investor should buy, sell, or hold his position. The optimal policy for the multi-period problem is, unfortunately, more complicated, but with numerical examples, we are able to show that a heuristic based on a single period policy performs quite well. In the third model, we study the mean-reversion effect in the stock market. The market efficiency theory implies that prices respond quickly and accurately to relevant information in the stock market. However, there is a great deal of debate over the efficient market hypothesis with a large amount of empirical evidence both supporting and contradicting the argument. Mean reversion in stock prices would indicate that this theory is largely incorrect, and as such, we examine the China A-share market for this phenomenon. An analysis of 700 stocks over a 6-year period shows that there is a significant mean reversion effect under the appropriate horizon.